Chemical Engineering Thermodynamics MCQ Questions & Answers | Chemical Engineering

Chemical potential acts as a driving force or potential difference to achieve chemical equilibrium like temperature acts as a driving force or potential difference for heat transfer. Higher the potential higher is the transfer.
The chemical potential when we expressed in terms of gibbs free energy it can be defined as partial molar gibbs free energy.
$$\mu = {\left( {\frac{{\partial nG}}{{\partial {n_j}}}} \right)_{T,P,{n_i}}}$$
Since partial molar gibbs free energy is an intensive property chemical potential is an intensive Property.

We know the property relation $$dG=VdP-sdT$$     for constant temperature $$dT=0$$
For an ideal gas
$$\eqalign{ & dG = VdP \cr & dG = \frac{{RT}}{P}dP \cr & \Rightarrow dG = RTdlnP \cr} $$
For a real gas also if we want to describe the relation in the same functional form we express it as $$dG = RTd \,ln\, f \Rightarrow d\mu = RTd \,ln\, f$$       where $$f=$$ fugacity, that means we buried the entire non ideality in this term fugacity. The term fugacity is also called as effective pressure.

Since for an ideal gas mixture : $$fugacity= pressure$$
\[\begin{array}{l} d\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over G} = RTdlnP\\ \Rightarrow d{\mu _i} = RTdlnP \end{array}\]

Boiling of a liquid is obviously accompanied by vapor pressure of the liquid at that temperature. Since boiling will occur when the liquid exhibited vapor pressure is equal to the external pressure imposed on that liquid.

Law of corresponding states : at same reduced properties all the gases behaves similarly. This is the statement of corresponding states and the reduced property is defined as the state variables of a fluid scaled by the state properties at its critical point.

As above the critical point there is no demarcation between the liquid and vapor we call the matter as gas.

First law of thermodynamics sates that energy can’t be destroyed instead it converts from one form to another form only. The two forms of energy in transits are heat and work with which the system contacts the surroundings there by changing its internal energy:
If we express this in mathematical form:
\[\delta Q=dU+\delta W\]
Where,
\[\delta Q=\text{ heat given to the system}\]
\[\delta W=\text{work done by the system}\]

Since to obtain the maximum work we have to use an reversible heat engine for an reversible heat engine operating between two reservoirs the efficiency is given by:
$$\eqalign{ & \mathop \eta \limits^\iota = \frac{W}{{{Q_1}}} = \frac{{{T_1} - {T_2}}}{{{T_1}}} \cr & \Rightarrow W = 1000\left( {\frac{{300 - 100}}{{573}}} \right) \cr & \Rightarrow W = 349J \cr} $$
Here $${{T_1}}$$ and $${{T_2}}$$ are temperatures in thermodynamic scale or kelvin temperatures.

For a real gas the $${C_V}$$ has an weak relationship with volume and pressure in many cases this relation can be neglected and depends only on temperature whereas for ideal gases $${C_V}$$ is solely dependent on temperature.
The usually relationship is given by $${C_V} = a + bT + C{T^2} + \,\,...$$     and these constants $$a, b, c…$$ varies from gas to gas.